§ 1.1 Field of the Invention
The present invention concerns signal processing. More specifically, the present invention concerns a low-pass filter that may be used in direct conversion transceivers.
§ 1.2 Related Art
Data communications and signal processing are introduced in § 1.2.1 below. Then, filters, including mathematical representations and different types of filters, their uses and their limitations are introduced in § 1.2.2.
§ 1.2.1 Signal Processing
Voice signals (referred to as v(t)) may be measured in the time domain. For analysis purposes sometimes it is more convenient to consider voice signals in the frequency domain. The voice signal in the frequency domain is represented by V(ω). (Following convention, lower case letters are used when describing a signal in the time domain, and capital letters are used when describing a signal in the frequency domain.) The time domain representation and the frequency domain representation of the same signal look different from each other, but they express the same information.
Through a processing of “mixing”, in the time domain, it is possible to “shift”, in the frequency domain, the voice signal V(ω), from dc (ω=0), to anywhere along the frequency axis. In order to shift the voice signal, V(ω), along the frequency axis, an oscillating signal x(t)=A cos(ω0t), is mixed with the voice signal, v(t). The amplitude of x(t) is “A”, and the frequency of x(t) is ω0. The oscillating signal, X(ω), in the frequency domain, comprises two dirac impulse functions located at the frequency of x(t), i.e., ω0 and −ω0.
Mixing v(t) and x(t) in the time domain generates a mixed signal b(t). In the frequency domain, B(ω) appears to be two V(ω) functions, shifted in the positive and negative directions so that the two V(ω) functions are centered around the positions of the dirac impulse functions. That is, one instance of V(ω) is centered at ω0 and another instance is centered at −ω0. This shifted signal is called B(ω).
Using the above described technique with a second voice signal (referred to as M(ω) and a second signal (referred to as G(ω) oscillating at a different frequency, it is possible to transmit both of the voice signals over one transmission medium using different frequency bands (e.g., radio). When m(t) and g(t) are mixed in the time domain, M(ω) is shifted to the left and the right to center around ω1 and −ω1. This shifted signal is called K(ω).
The time domain signals k(t) and b(t) can be added together, and in ideal conditions, l(t) would be obtained. In the frequency domain, L(ω) comprises the two voice signals lying in separate frequency bands and not interfering with each other. This combined signal l(t) can then be transmitted over a single transmission medium. Once l(t) is received by a device, the device can use a filter to isolate the channel (and therefore the signal) that is desired. A general discussion on the background of filters is given in the next section.
§ 1.2.2 Filters and Their Use in Transceivers
Filters have many uses in the field of signal processing. For example, as known in the art and just described in § 1.2.1 above, multiple channels of data can be mixed together and transmitted over a single transmission medium using one or some of a plurality of different processing techniques. In some situations (e.g., when channels are separated into frequency (ω) bands), filters may be used (e.g., at a receiver) to extract a desired channel by suppressing the other channels. The filtering operation also helps to suppress noise that may have been introduced into the signal.
Three basic categories of filters include high-pass filters, which pass channels in high frequencies; low-pass filters, which pass channels in low frequencies; and band-pass filters, which pass a specific frequency band (e.g., to isolate one channel of information).
A filter's characteristics or frequency response can be modeled mathematically, through its transfer function, H:
  H  =            Output      Input        =                  B        ⁡                  (          ω          )                            A        ⁡                  (          ω          )                    The root of the dominator, A(ω), of the transfer function are called the “poles” of a filter and the root of the numerator, B(ω), of the transfer function are called the “zeros” of a filter.
Filters may be real or complex. Real filters have poles that are symmetrical with respect to dc (ω=0), i.e., having one pole at ω=a, and another pole at ω=−a. Complex filters may have effective poles that are not necessarily symmetrical with respect to dc. The position of the poles is one factor that determines the frequencies a filter will pass. As mentioned earlier, low-pass filters pass frequencies around dc. Therefore, using the symmetric nature of real filters, a low-pass filter can be implemented using symmetric poles located close to dc. One use of low-pass filters is in direct conversion transceivers, as will be discussed further below.
As mentioned earlier, multiple channels of data can share a single transmission medium, but a receiver (e.g., a radio) may desire data from one channel. Therefore, to isolate the desired channel for processing, transceivers typically perform at least three operations on the received signal: (1) the undesired channels are filtered out; (2) the desired channel is “shifted” to dc, where it can be processed; and (3) the signal is amplified. The order of the operations depends on the design of the receiver. Shifting a signal may be accomplished by mixing the signal with a local oscillator signal.
In superheterodyne transceivers, the input signal (e.g., a Radio Frequency (“RF”) signal) is amplified and filtered. Then, the filtered RF signal is shifted to an intermediate frequency (“IF”) where it is passed through a highly selective filter and substantially amplified before it is shifted to dc for processing.
Direct conversion transceivers use techniques to avoid having to use an IF, thereby saving power, cost and allowing for a smaller physical design for some applications (like GSM). A part of an exemplary direct conversion receiver is illustrated in FIG. 1. The receiver 100 receives an input signal, xrf, and includes two quadrature related (separated in phase by 90°) local oscillator signals, lo1 (“I”), lo2 (“Q”), two mixers 105, 110, and two real low-pass filters, 115, 120.
An exemplary operation of the direct conversion receiver 100, which uses real low-pass filters, will now be discussed, As shown in FIG. 1, an input signal, xrf is applied to two paths. The mixers 105, 110 mix the input signal xrf with two local oscillator signals that are quadrature in nature (lo1 (I) and lo2 (Q)). The two resulting signals, x1 and x2, are separately filtered by two different low-pass filters 115, 120. Then, the filtered signals, y1 and y2, are processed to reform the transmitted signal in the known manner.
The two quadrature paths, I and Q, allow the direct conversion receiver to avoid having to use an IF. The following discussion describes, in theoretical terms, why a direct conversion receiver does not need to use an IF. When two local oscillator signals in a forward-quadrature relationship are added in the frequency domain (e.g., using the complex operator “j”:Xc(ω)=F{x1+jx2}), the two dirac impulse functions on the negative side cancel each other out, and the dirac impulse functions on the positive side add together to form a dirac impulse function with a doubled amplitude. Note that this combination results in a single dirac impulse function. Therefore a signal mixed with the single dirac impulse function is shifted in one direction. Using a reverse-quadrature pair if is possible to shift a received signal in the opposite direction. Direct conversion transceivers use this concept to shift the received signal to dc.
FIGS. 2 and 3 illustrate ideal direct conversion using the single dirac impulse function. FIG. 2 illustrates an exemplary received signal, RF(ω). The top graph of FIG. 3 illustrates the effective local oscillator signal LOc(ω) of a direct conversion receiver in ideal conditions, i.e., a single dirac impulse function. The lower graph of FIG. 3 shows the original signal, RF(ω), shifted to center around the dirac impulse function.
Unfortunately, the characteristics of direct conversion transceivers are not ideal. DC offsets, even-order distortion, flicker noise, LO leakage, I/Q imbalance, and imperfect filtering in direct conversion transceivers are some known sources of such non-ideal behavior. I/Q imbalance is introduced below in § 1.2.2.1. Leakage distortion, due to mismatches in the components used in the real filters, is introduced in § 1.2.2.2 below.
§ 1.2.2.1 I/Q Imbalance
Referring back to the direct conversion receiver of FIG. 1, slight differences in the I/Q relationship of LO1 and LO2, and I and Q signals that are not exactly in quadrature cause I/Q imbalance. This I/Q imbalance is illustrated by a small dirac impulse function at ωlo in the top graph of FIG. 4—the larger dirac impulse function at −ωlo is desired. For example, in the ideal case when two local oscillator functions are added together, the dirac impulse functions on the positive frequency side should cancel out perfectly, leaving just one dirac impulse function. However, I/Q imbalance causes an imperfect cancellation creating a small unwanted dirac impulse function on the positive frequency side. As illustrated in the lower half of FIG. 4, this small dirac function causes a small portion of the original signal to be shifted in the opposite direction, and a small amount of overlapping to occur at dc, creating distortions.
§ 1.2.2.2 Leakage Distortion—Mismatched Real Filters
Filter (component) mismatches also cause problems. If the components of filters 1215, 1220 are not perfectly matched, (i.e., if the transfer functions do not match—H1(ω) H2(ω)), then a non-zero transfer function, Hdf(ω), contributes to a leaked (undesired or difference) output component. Even when the filter components are fabricated at the same time and on the same integrated chip, component mismatch of 0.2% to 0.5% or even larger may still occur. A parallel model of an imperfect low-pass filtering operation is illustrated in FIG. 5. The top branch represents the common component, hcm, of H1(ω) and H2(ω), which produces the desired output. The bottom branch represents the difference component, hdf, between H1(ω) and H2(ω), which produces the leaked signal.
FIGS. 6–9 illustrate an imperfect low-pass filtering operation (even assuming no I/Q imbalance in the LO signals). FIG. 6 illustrates an exemplary received signal. In FIG. 7, ideal I/Q mixing is assumed, and the signals are only shifted in one direction. In FIG. 8, the shifted signals are filtered by imperfect real filters. The results are the desired signal illustrated in the top graph, and a leaked signal illustrated in the bottom graph. As shown in the imperfect filtering model of FIG. 5, the two resulting signals are added together (in a complex sense). FIG. 9 illustrates the distorted output signal of an imperfect low-pass filtering operation.
In view of the above discussion, there is a desire for reducing the consequences (e.g., leaked signal) associated with mismatched real filters. More specifically, there is a desire for methods and apparatus that can perform low-pass filtering that is less sensitive to mismatches in filter component values.